A roadway rises 4 ft for every 14 ft along the road. What is the angle of inclination of the roadway? The angle of inclination of the roadway is \( \square^{\circ} \). (Round to one decimal place as needed.)

To find the angle of inclination of the roadway, we can use the tangent function. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle. Given: - The roadway rises 4 ft for every 14 ft along the road. Let's denote: - The rise of the roadway as \( h = 4 \) ft - The run of the roadway as \( r = 14 \) ft The tangent of the angle of inclination (\( \theta \)) can be calculated as: \[ \tan(\theta) = \frac{h}{r} \] Substitute the given values: \[ \tan(\theta) = \frac{4}{14} \] Now, we can calculate the angle of inclination by finding the inverse tangent (arctan) of the ratio: \[ \theta = \arctan\left(\frac{4}{14}\right) \] Let's calculate the angle of inclination. Calculate the value by following steps: - step0: Calculate: \(\arctan\left(\frac{4}{14}\right)\) - step1: Reduce the fraction: \(\arctan\left(\frac{2}{7}\right)\) The angle of inclination of the roadway is approximately \(0.2783\) radians. To convert this to degrees, we can use the fact that \(1\) radian is approximately equal to \(57.2958\) degrees. Let's convert \(0.2783\) radians to degrees. Calculate the value by following steps: - step0: Calculate: \(0.2783\times 57.2958\) - step1: Multiply the numbers: \(15.94542114\) The angle of inclination of the roadway is approximately \(15.9\) degrees. Therefore, the angle of inclination of the roadway is \(15.9^{\circ}\).